Image sequence texture: no preview?
Unfortunately yes, that is the expected behavior (or call it a limitation, or a missing feature, or a bug...). Images used as part of the material currently refresh only on rendered view in Cycles.

If you switch back to Material Shading or any of the other OpenGL shading views int he viewport, the material will only show last image displayed in rendered view.

Editing the material will also force a refresh, but only for the current frame.

As an alternative (or to use as reference) you use an empty as image and use an image sequence, or video file, it will refresh correctly regardless of shading mode in the viewport. (see this link: https://blender.stackexchange.com/a/13897/1853) 

Images used as background will also refresh fine.

Note that images used as background and empties used as images are meant for reference only, and will display in the 3D viewport but are not renderable.